Method for determining load capacitance

ABSTRACT

A method for optimal driver selection uses a cost function that is based on the non-linear delay characteristics and the stage gain of the candidate drivers. The cost function operates to select an optimal driver for driving the predetermined capacitive load which. simultaneously minimizes the delay and the amount of input capacitance introduced. In one embodiment, a method for selecting a driver for driving a load capacitance from a group of drivers includes: computing for each driver a cost based on a cost function associated with the driver, and selecting the driver having the smallest cost. The cost function is directly proportional to a delay of the driver and inversely proportional to the logarithm of a stage gain of the driver. In another embodiment, the stage gain is an output capacitance driven by the driver (the load capacitance) divided by an input capacitance of the driver.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a division of U.S. patent application Ser.No. 10/022,747 filed on Dec. 14, 2001, now U.S. Pat. No. 6,754,877,entitled “Method for Optimal Driver Selection”, incorporated herein byreference.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is related to the following concurrently filedand commonly assigned U.S. patent applications: Ser. No. 10/023,329entitled “Method for Balanced-Delay Clock Tree Insertion,” by A.Srinivasan and D. Allen, Ser. No. 10/022,751 entitled “Method forDetermining A Zero-Skew Buffer Insertion Point,” by A. Srinivasan, andSer. No. 10/022,743 entitled “Method for Match Delay Buffer Insertion,”by A. Srinivasan and D. Allen

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a system and method for integrated circuitdesign, and more particularly to a system and method for inserting aclock tree in an integrated circuit design.

2. Description of the Related Art

A standard cell-based integrated circuit is designed using a library ofbuilding blocks, known as “standard cells.” Standard cells include suchelements as buffers, logic gates, registers, multiplexers, and otherlogic circuits (“Macros”).

FIG. 1 shows a typical design process or “design flow” 100 that anintegrated circuit designer would use to design a standard cell-basedintegrated circuit. Referring to FIG. 1, the designer provides afunctional or behavioral description (101) of the integrated circuitdesign using a hardware description language (HDL). In addition, thedesigner specifies timing and other performance constraints which theintegrated circuit design must comply. The designer also selects astandard cell library to implement the design. Typically, the standardcells in the library are designed to the requirements of a targetintegrated circuit fabrication technology. Often, each cell is alsocharacterized in the library to provide performance parametric valuessuch as delay, input capacitance and output drive strength.

At step 102, the designer uses a “synthesis tool” to create from the HDLdescription 101 a functionally equivalent logic gate-level circuitdescription known as a “netlist” (103). The elements of the netlist areinstances of standard cells selected by the synthesis tool from thestandard cell library in accordance with functional requirements and theperformance constraints.

Next, a place and route tool is used to create a “physical design” basedon the gate-level netlist (103). The place and route tool uses aphysical library 104 containing the physical design of the standardcells in the standard cell library. In operation, the place and routetool places the standard cell instances of the netlist onto the “siliconreal estate” and routes conductor traces (“wires”) among these standardcell instances to provide for interconnection. Typically, the placementand routing of these standard cell instances are guided by costfunctions, which minimize wiring lengths and the area requirements ofthe resulting integrated circuit.

At step 105, an initial placement of the integrated circuit design isperformed and a placement file 106 is generated containing the placementinformation of all standard cell instances of the design. In design flow100, after the initial placement, certain pre-route optimization isperformed to ensure that the current placement meets the timingconstraints imposed by the design (step 107). Physical optimizationoperates by recursively performing timing analysis, detecting timingviolations and performing corrections (such as by introducing delays orby speeding up a signal path). The physical optimization tasks generallyinclude correcting maximum delay violations and minimum delayviolations. After the physical optimization is completed, a modifiednetlist 108 and a modified placement file 109 are generated.

Then, at step 110, a clock tree for the integrated circuit design iscreated and inserted into the design. Most integrated circuit designs,such as those employing sequential logic, are driven by one or moreclock signals. In the functional or behavior description of the design,the clock signal is merely represented as a wire distributing the clocksignal from a clock input terminal to all nodes within the integratedcircuit design receiving the clock signal. In the present description,nodes within an integrated design driven by the clock signal is referredto as “clock signal endpoints” or “clock endpoints.” A clock endpoint istypically an electrical terminal or a “pin” of a standard cell instance.The clock tree insertion step (110) operates to transform the wirerepresenting the clock signal into a buffer tree so that the clocksignal from the input terminal can drive all endpoints within the timingconstraints of the design. The clock tree insertion step generates amodified netlist 112 including the buffers of the clock tree and amodified placement file 113 including the placement information of thebuffers in the clock tree.

After physical optimization is performed and the clock tree is inserted,the placement of the integrated circuit can be legalized. Then, at step114, the design can be routed so that all standard cell instances,including the clock tree, are connected with conductor traces (wires).Subsequently, a design verification step 115 is carried to ensure thatthe design meets the timing constraints specified for the overall designFor instances, with the wires of the integrated circuit routed, a moreaccurate set of parasitic impedance values in the wires can beextracted. Using the extracted parasitic impedance values, a moreaccurate timing analysis can be run at step 115 using a static timinganalyzer (STA). If the physical design meets timing constraints, thedesign process is complete. Otherwise, steps 105 to 114 are repeatedafter appropriate modifications are made to the netlist and theperformance constraints.

As described above, the clock tree insertion step operates to transformthe wire carrying the clock signal into a buffer tree propagating theclock signal from the clock input terminal throughout the design subjectto certain predefined timing constraints. The timing constraintsbasically ensure that all clock signals arrive at about the same time atdifferent nodes of the integrated circuit receiving the clock signal. Ingeneral, timing constraints for a clock tree include the maximum andminimum insertion delay time, the clock skew and the clock transitiontime.

Techniques for constructing a clock tree are well known. The prevalentmethod used in integrated circuit design is the construction of an“H-Tree.” FIG. 2 illustrates an exemplary H-Tree in an integratedcircuit for distributing the clock signal. The principle behindconstructing an H-tree is to distribute the clock signal so as tobalance the loading of the clock tree. Referring to FIG. 2, anintegrated circuit 118 is shown including multiple number of clocksignal endpoints scattered throughout the integrated circuit. Forexample, an endpoint 123 denotes one of the many clock endpoints ofintegrated circuit 118. FIG. 2 is an abstract representation ofintegrated circuit 118 and is provided to illustrate the positions ofthe clock endpoints in the integrated circuit. As mentioned above, anendpoint of a clock signal is the electrical terminal or the pin of astandard cell instance receiving the clock signal.

The clock signal is coupled to integrated circuit 118 through a rootnode. In FIG. 2, an H-tree 120 is constructed connecting the clocksignal from the root node to the clock endpoints. Typical H-treeconstruction starts by dividing the integrated circuit into regions,each region containing a number of endpoints. In FIG. 2, four regionsare defined. Then, an approximate center of each region is determinedand the center is used as a point for buffer insertion. For example, abuffer insertion point 124 in a region 122 (the lower-right region) ofintegrated circuit 118 is identified. Then, each region is furtherdivided and the approximate center is identified to define bufferinsertion points at the next level of the H-tree. For example, a bufferinsertion point 126 is identified for a sub-region within region 122.H-tree 120 can be recursively refined to a required level in order todrive all endpoints within the predefined timing constraints.

The benefits of using an H-tree for clock distribution is that, byrecursively building the H-tree, the same wire distance can bemaintained between the root node to any of the endpoints. When distanceis used as a proxy for load capacitance, equal distance means equal loadcapacitance at each endpoint. Because insertion delay of the clocksignal at any endpoint is directly proportional to load capacitance, theH-tree is constructed so that the clock signal delay to any of theendpoints is approximately the same. In this manner, the H-treemethodology constructs a clock tree meeting the timing constraints.

In the construction of the H-tree, the same buffer is used at eachbuffer insertion point to ensure balanced loading. Thus, another benefitof the H-Tree is that the integrated circuit design tends to be morestable across fabrication process variations and operational environmentvariations (such as temperature) because the same buffers are used.

However, the H-tree methodology for constructing a clock tree hasseveral disadvantages. First, it is difficult to construct an H-tree tobalance the loading between a region with dense endpoints and a regionwith sparse endpoints. Often, in an effort to achieve balanced loadthrough balanced distance, the H-tree methodology may unnecessarily addextra loading to the sparse regions. The extra loading effectivelyincreases the total loading of the clock tree, creating a clock treethat is “larger” than necessary.

Referring to FIG. 2, region 122 of integrated circuit 118 may be asparse region containing few clock signal endpoints. On the other hand,a region 121 above region 123 may be a dense region containing many moreclock signal endpoints. Because the H-tree is optimized to achievebalanced load by balancing the wire distance, the same size and sameamount of buffers will be used to drive endpoints in both the dense andthe sparse regions. However, in the dense region, the buffers need todrive a large number of endpoints while in the sparse region, thebuffers only need to drive a small number of endpoints.

FIGS. 3 a and 3 b illustrate the situations when an H-tree is used todrive endpoints in a dense region and in a sparse region. In FIG. 3 a, abuffer 132 a is in a dense region and thus has to drive a large numberof endpoints, represented by a capacitor C_(large). In FIG. 3 b, abuffer 132 b, same type of buffer as buffer 132 a, is in a sparse regionand thus has to drive only a small number of endpoints, represented by acapacitor C_(small). When C_(large) is much greater than C_(small), theH-tree is not balanced because the same buffers (132 a and 132 b) aredriving different loads. The common solution to the dense/sparse regionsproblem in constructing an H-tree is to add dummy load to buffers in thesparse region so that the clock tree is balanced. Referring to FIG. 3 b,a dummy load, represented by capacitor C_(dummy) is added in parallel tocapacitor C_(small) so that the total capacitance of the two capacitorsequals the capacitance of C_(large).

Because of the addition of the dummy load, the clock tree is made largerfor driving a larger load created merely for the purpose of balancingthe loading of the clock tree. As a result, the clock tree tends to beslower because the clock tree has to drive a large amount of load. Thus,the H-tree methodology trades off clock insertion delay for the entiretree in order to gain a clock tree with balanced load. Furthermore, alarger clock tree requires more silicon area to implement, resulting inincreased manufacturing cost.

Second, balancing the load does not always imply balancing the insertiondelay of the clock signal. The H-tree methodology assumes a linear,proportional relationship between wire distance and load. However, asmall change in wire distance may translate into a large change in loadcapacitance. Therefore, by using wire distance as proxy for loading inconstructing the clock tree, unpredictable clock signal delays mayresult.

As integrated circuit dimensions continue to shrink, the aforementioneddisadvantages and tradeoffs in clock tree constructions becomeunacceptable. Therefore, it is desirable to provide an improved methodfor clock tree construction which can avoid the aforementioneddeficiencies so that a clock tree can be constructed and optimized tomeet timing constraints.

SUMMARY OF THE INVENTION

A method for optimal driver selection uses a cost function that is basedon the non-linear delay characteristics and the stage gain of thecandidate drivers. The cost function operates to select an optimaldriver for driving the predetermined capacitive load whichsimultaneously minimizes the delay and the amount of input capacitanceintroduced.

In one embodiment, a method for selecting a first driver for driving aload capacitance from a group of drivers includes: computing, for eachdriver in the group of drivers, a cost based on a cost functionassociated with the driver for driving the load capacitance, andselecting the driver having the smallest cost as the first driver. Thecost function is directly proportional to a delay of the driver andinversely proportional to the logarithm of a stage gain of the driver.

In another embodiment, the stage gain is an output capacitance driven bythe driver divided by an input capacitance of the driver, where theoutput capacitance is the load capacitance.

The present invention is better understood upon consideration of thedetailed description below and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a typical design process or a “design flow” that anintegrated circuit designer would use to design a standard cell-basedintegrated circuit.

FIG. 2 illustrates an exemplary H-Tree in an integrated circuit fordistributing the clock signal.

FIGS. 3 a and 3 b illustrate the situations when an H-tree is used todrive endpoints in a dense region and in a sparse region of clock signalendpoints.

FIG. 4 is a block diagram of a clock tree insertion system according toone embodiment of the present invention.

FIG. 5 is a flow chart illustrating the clock tree insertion processemployed by the clock tree insertion system of FIG. 4 according to oneembodiment of the present invention.

FIG. 6 illustrates an integrated circuit including two conventionallocations for a root node of a clock tree.

FIG. 7 illustrates a root node of a clock tree specified according toone embodiment of the present invention.

FIG. 8 is a flow chart illustrating the process for constructing a clocktree that minimizes the maximum insertion delay at any endpointsaccording to one embodiment of the present invention.

FIGS. 9 a and 9 b illustrate the operation of the clustering operationin grouping clock endpoints of an integrated circuit design intoclusters.

FIG. 10 is a flowchart illustrating the clustering operation accordingto one embodiment of the present invention.

FIG. 11 illustrates a clock tree constructed to minimize the maximuminsertion delay using the clock tree insertion process of the presentinvention.

FIG. 12 is another representation of the clock tree in FIG. 11illustrating the connection of the clock tree to sequential logic gatesas clock endpoint.

FIG. 13 is a plot of the arrival times for the clock endpoints of theclock tree in FIG. 11.

FIG. 14 includes three timing diagrams illustrating the arrival times atthe clock endpoints of clock tree 320 at various steps of the clock treeinsertion process.

FIG. 15 is a flow chart illustrating the clock skew correction processaccording to one embodiment of the present invention.

FIG. 16 is a plot of the arrival times for various skew intervals forthe clock tree in FIG. 11.

FIG. 17 illustrates the process for apportioning ΔDelay values accordingto one embodiment of the present invention.

FIG. 18 is a flow chart illustrating the min delay correction processaccording to one embodiment of the present invention.

FIG. 19 is a flowchart illustrating the match-delay buffer insertionmethod according to one embodiment of the present invention.

FIGS. 20 a and 20 b illustrate the operation of the match-delay bufferinsertion method of the present invention.

In the present disclosure, like objects which appear in more than onefigure are provided with like reference numerals.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In accordance with the principle of the present invention, a clock treeinsertion system constructs a clock tree in an electrical design, suchas an integrated circuit design, using a balanced delay approach so thata fast clock tree with predictable delay can be realized. First, theclock tree insertion system constructs a clock tree to minimize theworst insertion delay to any clock endpoint. Then, the clock treeinsertion system introduces delays at the nodes with the fastest clockarrival time to ensure that the clock tree will meet target clock skewand target minimum delay constraints. A clock tree thus constructed hasdelay and skew values that can meet tighter timing constraints. Also, bybalancing the delay directly, the clock tree insertion system cangenerate a clock tree with predictable delay and improved stability.Furthermore, the clock tree is optimized without the need to introducedummy loads. Therefore, a clock tree constructed according to the clocktree insertion system of the present invention consumes less siliconarea and less power in operation.

The clock tree insertion system can be incorporated into any integratedcircuit design flow such as design flow 100. Design flow 100 isillustrative only and the clock tree insertion system of the presentinvention can be applied in other design flows for designing anintegrated circuit. In one embodiment, the clock tree insertion systemis applied in an integrated circuit design flow using aninterconnect-driven optimization process and incremental place and routefor physical design modification. Such a design process is described incopending and commonly assigned U.S. patent application Ser. No.09/516,489, entitled “Method And Apparatus For Interconnect-DrivenOptimization of Integrated Circuit Design,” of Douglas Kaufman et al.,filed Mar. 1, 2000, which patent application is incorporated herein byreference in its entirety. Basically, the clock tree insertion systemand method can be applied to any integrated circuit design flow fortransforming a clock signal, represented as a wire in an integratedcircuit design, to a buffer clock tree based on specified timingconstraints.

Clock Tree Insertion System Overview

FIG. 4 is a block diagram of a clock tree insertion system according toone embodiment of the present invention. Referring to FIG. 4, clock treeinsertion system 200 includes a max delay solver module 202, a skewsolver module 203 and a min delay solver module 204. Clock treeinsertion system 200 can be implemented on a computer, such as a SPARCstation available from Sun Microsystems, Inc., Palo Alto, Calif. In thepresent embodiment, a designer interacts with system 200 using agraphical user interface (GUI) (not shown). Of course, other means forinteracting with clock tree insertion system 200 can be used, such asusing operating system level commands including UNIX command line, as iswell known in the art.

Clock tree insertion system 200 receives four categories of input files.First, system 200 receives information describing an integrated circuitdesign to be processed. The integrated circuit design can be presentedin the form of a netlist 206 and a placement file 205 generated from thenetlist. The netlist and placement files can be expressed in anystandard industry format, such as the LEF and DEF file formats supportedby Synopsys, Inc. Netlist file 206 includes connection information forone or more clock signals driving the integrated circuit design. Asdescribed above, prior to clock tree insertion, the clock signal isrepresented in the netlist merely as a single wire connecting a clockinput terminal receiving the clock signal to all of the clock endpointsassociated with that clock signal.

Clock tree insertion system 200 also receives a specification 208defining the timing and physical constraints for the integrated circuitdesign. The timing and physical constraints can be expressed in anystandard industry format, such as those formats used in the “Primetime”tool from Cadence Design Systems, Inc. The timing constraints inspecification 208 include the overall timing constraints for the design.The timing constraints can include required arrival time, required delaytime and transition time of the signals in the design. The physicalconstraints describe where instances of standard cells can be placed inthe integrated circuit, that is, the locations of the rows for cellplacement and the locations of the routing channels. The physicalconstraints also specify the locations of obstructions, if any, for cellplacement in the integrated circuit design. An obstruction can include aMacro element such as a memory block where a standard cell instancecannot be placed.

Clock tree insertion system 200 further receives a clock treespecification 210 defining the characteristics of the clock tree to beconstructed and included in the integrated circuit design. Details ofclock tree specification 210 will be described in more detail below.

Finally, clock tree insertion system 200 utilizes a number of libraryfiles providing information describing the technology used to fabricatethe design and the standard cells that are available for constructingthe clock tree. In the present embodiment, system 200 receives aplacement library 212 including floorplan information for the integratedcircuit design. Placement library 212 specifies the global physicalconstraints for the integrated circuit design as defined by thefabrication process. For example, placement library 212 defineslocations where power buses for the integrated circuit are to be placedand locations for placing the standard cells.

System 200 also receives a technology Library 214 specifying thefabrication process to be used for the design. Technology library 214defines the properties of the different layers (metal and polysilicon)in the fabrication process, including the electrical characteristicssuch as resistance per unit length and capacitance per unit length ofeach layer.

Finally, system 200 receives a cell library 216 including the timing andphysical information for each standard cell in the library. The physicalinformation describes, among other things, where the input/outputterminals (pins) are at the boundary of each standard cell. The timinginformation describes, among other things, the timing delay through thecell, and the output signal transition time as a function of outputloading.

Clock tree insertion system 200 operates to construct a buffer tree fordistributing the clock signal throughout the integrated circuit designwithin specified timing constraints. Clock tree insertion system 200generates as output files a modified netlist 218 including the buffersforming the clock tree and a modified placement file 220 including theplacement of the buffers of the clock tree in the integrated circuitdesign.

In the present description, a clock tree is described as a “buffer tree”including an array of buffers as the drive elements of the clock signal.In actual implementation, the buffer tree can be constructed usingnon-inverting buffers (generally referred to as “buffers”) or invertingbuffers (generally referred to as “inverters”), or a combination ofboth, as long as the polarity of the clock signal is maintained. One ofordinary skill in the art would appreciate that any buffer in a clocktree can be replaced by a pair of inverters and vice versa. In thefollowing description, the drive elements of a clock tree will bereferred to as “buffers” exclusively. However, it is understood that“buffers” in the present description can include both non-invertingbuffers (buffers) or inverting buffers (inverters). Basically, buffersand inverters can be used interchangeable in constructing a clock treeas long as the polarity of the clock signal is maintained.

Furthermore, in the present description, the integrated circuit designis assumed to have one clock signal only and clock tree insertion system200 is used to insert one clock tree to distribute the single clocksignal. However, in other embodiments, the integrated circuit design mayinclude more than one clock signal. Clock tree insertion system 200 canbe used to insert one or more clock trees for one or more correspondingclock signals in an integrated circuit design. The several clock treescan be constructed simultaneously or the clock tree insertion system canbe repeatedly applied to construct one clock tree at a time. The presentdescription involving constructing one clock tree is illustrative only.

Clock Tree Insertion Process

FIG. 5 is a flow chart illustrating the clock tree insertion processemployed by clock tree insertion system 200 according to one embodimentof the present invention. The clock tree insertion system and processwill be described with reference to FIGS. 4 and 5. Referring to FIG. 5,at step 240, clock tree insertion system 200 receives a netlist file(206) and a placement file (205) for an integrated circuit design. Atstep 242, clock tree insertion system 200 receives a specification (208)defining the timing and physical constraints for the integrated circuitdesign. At step 244, clock tree insertion system 200 receives a clocktree specification (210) defining parameters for the clock tree to beinserted into the integrated circuit design.

As described above, system 200 also utilizes a number of library filesincluding placement library 212, technology library 124, and celllibrary 216. These library files can be made available to system 200each time a design is processed or the library files can be madecontinuously available to clock tree insertion system 200 while system200 processes a number of integrated circuit designs for constructingclock trees therein. Therefore, in one embodiment, the process flow inFIG. 5 may further include the step of providing the library files tosystem 200. In other embodiments, system 200 can access the libraryfiles continuously.

Clock Tree Specification

To construct a clock tree in an integrated circuit design, the designerspecifies the logical connections of the clock signal which isrepresented in the netlist as a wire connecting a clock signal to anumber of clock signal endpoints. The designer also provides a clocktree specification (step 244 of FIG. 5) defining parameters for theclock tree to be constructed so that the clock signal can be distributedthroughout the integrated circuit within specified timing constraints.The format and content of a clock tree specification are well known andtypically includes one or more of the following parameters:

(1) Root Node—The designer specifies the location of the “root node” forthe clock tree. The “root node” is defined as the starting point for theinsertion of the clock tree. FIG. 6 illustrates two conventionallocations for a root node of a clock tree. Referring to FIG. 6,integrated circuit 260 is illustrated with a clock input terminal (CLKpad) 262 receiving the clock signal and a clock tree 266. FIG. 6illustrates two conventional locations for placing the root node. First,the root node of clock tree 266 can be located at the clock inputterminal as shown by root node 264 a. Second, the root node of clocktree 266 can be located at an output terminal of a logic block fromwhich the clock signal is derived, as shown by root node 264 b.

When the root node is not placed at the clock input terminal of anintegrated circuit design, the conventional clock tree specificationtypically limits the placement of the root node at an output terminal ofa logic gate (such as root node 264 b). This placement limitation can beundesirable because the insertion of a clock tree at the output terminalof a logic gate can change the delay of the logic gate due to theloading introduced by the clock tree. Therefore, the delay of the clocksignal can change depends on the size and loading of the clock tree thatis inserted at root node 264 b.

In accordance with the present invention, system 200 allows a designerto specify the location of a root node of a clock tree at an inputterminal of a logic gate. FIG. 7 illustrates a root node of a clock treespecified according to one embodiment of the present invention.Referring to FIG. 7, an integrated circuit 270 includes a clock inputterminal 272 receiving a clock signal. The clock signal is coupled to alogic block 273 deriving the clock signal. A root node 274 for a clocktree 276 constructed for integrated circuit 270 can be specified at aninput terminal of an NAND gate 275. In this manner, the insertion ofclock tree 276 will not change the delay of the clock signal at rootnode 274.

As mentioned above, an integrated circuit design may include one or moreclock signals. When an integrated circuit design includes two or moreclock signals, a root node is specified for each clock signal.Furthermore, the designer may specify more than one root node for eachclock signal so that two or more clock trees can be constructed for asingle clock signal.

(2) Buffer List—The designer specifies in the clock tree specification alist of buffers (a buffer set) and inverters which can be used to buildthe clock tree. The buffer set can be a subset of the buffers andinverters that are available in cell library 216. The list generallyincludes buffers and inverters of a variety of sizes and drive strength.

(3) Timing Specification—The designer must specify the timingconstraints for the clock tree. Typically, the timing constraintsincludes the minimum insertion delay (min delay), the maximum insertiondelay (max delay), the maximum clock signal transition time (max trans)and the maximum clock skew (max skew) of the clock signal.

The minimum insertion delay requirement specifies the smallest delaytime for the clock signal to travel from the root node to any endpoint.That is, when the clock tree is constructed, the arrival time of theclock signal at any endpoints in the clock tree must be equal to orgreater than min delay.

The maximum insertion delay requirement specifies the largest delay timefor a clock signal to travel from the root node to any endpoint. Thatis, when the clock tree is constructed, the arrival time of the clocksignal at any endpoints in the clock tree must be equal to or less thanmax delay.

The maximum clock signal transition time requirement imposes limitationson the transition time or edge rate of the clock signal at any endpointof the clock tree. Thus, at any endpoint of the clock tree, thetransition time for the falling or rising edge of the clock signal mustbe equal to or faster than max trans.

The maximum clock skew requirement specifies the maximum difference (theclock skew) between the slowest arrival time and the fastest arrivaltime of the clock signal in the clock tree. Thus, the clock skew of theclock tree must be equal to or less than max skew.

In accordance with an embodiment of the present invention, clock treespecification 210 provided to clock tree insertion system 200 includesadditional parameters described below. The additional parametersdescribed below are optional and are included to aid in the constructionof the clock tree.

(4) Input Terminal Drive Strength—In accordance with the presentinvention, when the root node specified is at the input terminal of theclock signal (such as root node 264 a in FIG. 6), the clock treespecification of the present invention allows the designer to alsospecify a driving cell at the input terminal and specify the drivestrength of the driving cell. In one embodiment, the driving cell isspecified by including the driving cell in the netlist. In anotherembodiment, the driving cell is specified by incorporating thecharacteristics of the driving cell in the specification of the inputterminal.

The advantage of specifying a driving cell for a root node at an inputterminal is to allow a realistic representation of the input terminal tobe included in the clock tree specification. In conventional celllibraries, the input terminal is treated as an ideal terminal which iscapable of driving an infinite length of wire. In other words, the inputterminal is modeled as a perfect voltage source with zero outputresistance. However, in actual implementation, the input terminal,including a buffer and other input protection circuits, actually hasfinite drive strength and non-zero output resistance. Therefore, byspecifying the drive strength of a clock input terminal when the inputterminal is the root node, clock tree insertion system 200 is betterable to construct a clock tree appropriate for the drive capability ofthe input terminal.

(5) Heuristics—The designer may also specify various heuristics for usein the clock tree insertion process. For example, the designer mayspecify the distance measure to be used. Distance measurements commonlyused in integrated circuit designs include the Euclidean system, therectilinear (Manhattan) system and the sigma (statistical) system. Inaccordance with one embodiment of the present invention, a hybrid systemrepresenting a mix of the Euclidean and rectilinear systems may be used.

Construct a Clock Tree

Returning to FIG. 5, after step 244, clock tree insertion system 200 hasenough information to proceed with constructing a clock tree for theintegrated circuit design. In the present embodiment, the clock treeinsertion process consists of three steps. First, a clock tree isconstructed connecting the root node to all clock endpoints where theclock tree is constructed to minimize the maximum insertion delay (step246). The clock tree thus constructed must meet the max delayconstraint. Second, the clock tree is analyzed to determine if the clockskew constraint has been violated. If so, the clock skew violations arecorrected by inserting delays at buffer locations associated with thefastest arrival times (step 248). Finally, after correcting any clockskew violations, the clock tree is analyzed to determine if the arrivaltimes at any endpoints violate the min delay constraint. If so, the mindelay violations are corrected by inserting delays at buffer locationsat or near the root node (step 250). In constructing the clock tree, themaximum transition time constraint is considered at all three steps ofthe clock tree insertion process. That is, at each step of the process,the edge rate of the clock signal at any endpoint must meet max thetrans constraint before the clock tree is accepted. In this manner, aclock tree meeting timing constraints is constructed. The operation ofthe clock tree insertion process will now be described in detail.

Minimize Maximum Insertion Delay

At step 246, max delay solver module 202 in clock tree insertion system200 operates to construct a buffer tree to distribute the clock signalto clock endpoints that minimizes maximum insertion delay while meetingthe transition time constraint. In other words, the buffer tree isconstructed so that the clock signal will arrive at the farthestendpoint in as small a delay as possible and in any case, the delay mustbe less than the max delay constraint. Meanwhile, the buffer tree isconstructed to ensure that the clock signal transition time at anyendpoint does not exceed the max trans constraint. The balancing of themax delay and max trans constraints may require a buffer to be added toboost the edge rate of the clock signal even if the buffer may introduceadditional delay.

FIG. 8 is a flow chart illustrating the process for constructing a clocktree that minimizes the maximum insertion delay at any endpointsaccording to one embodiment of the present invention. Referring to FIG.8, at step 280, the clock endpoints for the clock tree is identified.Clock endpoints are nodes in the integrated circuit design driven by theclock signal. Generally, there are three types of endpoints. Endpointscan include the clock input terminal of sequential logic gates (such asflip-flops and latches) where the clock signal stops at the logic gates.Endpoints can also include an input terminal of any combinational logicgates (such as NAND and NOR gates) where the clock signal propagatesthrough the gate. Finally, endpoints may include input terminals at anyMacro blocks such as memory blocks which can be driven by one or moreclock signals.

After identifying the endpoints for the clock tree, a clusteringoperation is performed using the clock endpoints as clustering nodes(step 281). In the present description, “clustering nodes” refer toobjects to be clustered in the clustering operation. As will becomeapparent in the description below, clustering nodes may be clockendpoints or may be buffers (i.e., input nodes of buffers in the clocktree). The clustering operation is illustrated in FIGS. 9 a and 9 b andthe flowchart of FIG. 10.

Clustering Operation

FIG. 9 a is an abstract representation of an integrated circuit design290 after the initial placement of the standard cell instances in thenetlist of the design. A root node 293 has been specified for integratedcircuit design 290. In FIG. 9 a, the clock endpoints are shown as blackdots scattered throughout integrated circuit design 290. In actualimplementation, the standard cell instances are typically placed in rowsdefined by the physical constraints in specification 208 and therefore,the clock endpoints may not be randomly arranged as is shown in FIG. 9a. The placement of clock endpoints in FIG. 9 a is illustrative only andis provided to show the spatial relationships between the clockendpoints and between the root node and the clock endpoints.

Turning now to the clustering operation in step 281 where the clockendpoints are used as the clustering nodes. Referring to FIG. 10,clustering operation 300 starts by identifying the farthest clusteringnode from the root node and designating the farthest clustering node asthe current node (step 302). The current node is used as the seed pointfor forming a cluster. If two or more clustering nodes have the samefarthest distance from the root node, one of the nodes can be selectedarbitrarily as the farthest clustering node. Alternately, clusteringoperation 300 may switch to another distance metric and determine whichof the clustering node is farthest away from the root node.

In the present clustering operation, the farthest clustering node is thefarthest endpoint from the root node. Referring to FIG. 9 a, an endpoint291 is identified as the farthest endpoint (farthest clustering node)from root node 293 and is thus selected as the current node. Then, atstep 304, a clustering node near the current node is selected. Forexample, an endpoint 292 near endpoint 291 is selected.

Clustering operation 300 then determines at step 306 whether theselected node (endpoint 292) should be added to the cluster (the currentcluster) defined by the current node (endpoint 291). The criteria arebased on the timing and physical constraints for the design(specification 208) and for the clock tree (specification 210). In thepresent embodiment, the criteria include the buffer set that isavailable for building the buffer tree, as specified in the clock treespecification, and the maximum capacitate load that can be driven by thebuffers. The selected node can be added to the current cluster if theaddition does not cause max delay constraint and transition timeconstraint violations. Determination step 306 involves performing timinganalysis on the integrated circuit design.

In the clock insertion process of the present invention, timing analysisis repeatedly performed in the various steps of the process. The timinganalysis can be performed using any commercially available static timinganalysis tool. At each step, a full timing analysis for the entireintegrated circuit or an incremental timing analysis associated withnodes of interest can be performed as needed. One example of a statictiming analysis tool is ShowTime available from Sequence Design, Inc. ofSanta Clara, Calif.

To perform timing analysis, the integrated circuit design or the portionof the circuit of interest may need to be routed with wires so that wiredelay can be estimated. The routing can be performed using anycommercially available place and route tool, such as Silicon Ensemblefrom Cadence Design Systems, Inc. of San Jose. The place and route toolroute wires between circuit elements of interest so that the actualcapacitive load can be determined. In the present embodiment of thepresent invention, clock tree insertion system 200 uses a “route model”to estimate the actual wire routes and the effective capacitive loadingbetween circuit elements. Instead of performing actual routing, theroute model approximates the routing to determine the parasitic loading.The route model is, e.g., provided by PhysicalStudio from SequenceDesign, Inc., of Santa Clara, Calif.

In accordance with the present embodiment of the present invention, theinsertion delay of the clock signal is measured from the root node tothe output node of the logic gate driven by the clock signal. Forexample, when an endpoint is the clock input of an instance of aflip-flop, the insertion delay of the clock signal is the delay measuredfrom the root node to the Q (output) or NQ (inverted output) terminal ofthe flip-flop. In other embodiments, other schemes for measuringinsertion delay of the clock signal can be used. Furthermore, inaccordance with the present invention, the delay time is computed basedon the effective capacitive loading, instead of the wire length of thewires connecting the root node to the output terminal of interest.

At step 306, when clustering operation 300 determines that all timingand physical constrains are met, the selected node can be added to thecurrent cluster. At step 308, the selected node is added to the currentcluster and is marked so that the clustering node is taken out ofconsideration in the next iteration of the clustering operation. Theclustering operation continues by selecting the next node in theneighborhood of the current node (step 310). Steps 306 to 310 arerepeated to determine if another node can be added to the currentcluster. The process iterates until it is determined that a selectednode cannot be added to the current cluster. For example, when addingthe selected node will cause max trans violation because even thelargest buffer in the buffer set cannot drive all of nodes in thecluster including the newly selected node, the clustering operation forthe current cluster ceases and a cluster is formed (step 311). Referringto FIG. 9 a, a cluster 294 is formed by the operation of steps 304 to311.

After one cluster is formed, operation 300 proceeds by selecting thenext farthest clustering node as the current node (step 312). Forexample, an endpoint 295 in design 290 may be selected. If the nextfarthest clustering node is not the last node (step 314), steps 304 to311 are repeated until another cluster is formed based on the currentnode. If there are no more nodes to be clustered (step 314), theclustering operation based on the clock endpoints is completed (step316). FIG. 9 a illustrates the progress of clustering operation 300where several clusters have been formed around the perimeter ofintegrated circuit design 290. FIG. 9 b illustrates the completion ofthe clustering operation where all endpoints in integrated circuitdesign 290 have been grouped into a respective cluster.

FIG. 10 illustrates one embodiment of the clustering operation of thepresent invention. Other methods for clustering objects may be used inthe clock tree insertion method of the present invention. In oneembodiment, instead of selecting one neighboring clustering node at atime and determining if the selected node can be added to a currentcluster, the clustering operation can select a group of clustering nodesnear the farthest clustering node (the current node). The group ofclustering node is sorted by distance to the current node. Then, theclustering node nearest to the current node is tested to determine ifthe node should be added to the cluster using the criteria discussedabove. The process continues until the clustering nodes in the group isexhausted or a cluster is formed. When all clustering nodes areexhausted or when a new cluster is to be formed, the process proceeds byselecting another group of clustering nodes near the farthest clusteringnode.

Returning to FIG. 8, after the clustering operation based on the clockendpoints (step 281), the clock tree insertion process proceeds todetermine a buffer insertion point for each cluster (step 282). In oneembodiment, the geometric center of the area occupied by the cluster isused as the buffer insertion point. The geometric center is thearithmetic mean of the distances from the buffer insertion point to theendpoints within a cluster. In accordance with another aspect of thepresent invention, the buffer insertion point is positioned at a“zero-skew” point within the cluster. The determination of the zero-skewpoint within a cluster will be described in more detail below. FIG. 9 billustrates buffer insertion points for each of the clusters formed byclustering operation (step 281). For example, a buffer insertion point296 is selected for cluster 294.

Next, at step 283, a buffer for each cluster is selected from the bufferlist and the selected buffer is added to the buffer insertion pointidentified in the previous step. Traditional methods for bufferselection can be used. For example, in one traditional method, thebuffer can be selected to give a fanout factor of e. In otherembodiments, the selection process is carried out by computing a costfunction associated with each buffer in the buffer list, and selectingthe buffer with the best cost characteristics. The cost function can bebased on a variety of factors, such as the estimated insertion delaytime and the clock signal transition time provided by the buffer.

In accordance with another aspect of the present invention, a method foroptimal driver selection is used for selecting the buffer from a list ofcandidate buffers. The optimal driver selection method uses a costfunction based on the delay characteristic and the capacitive gain ofeach buffer is the buffer list. The capacitive gain is defined asC_(OUT)/C_(IN) where C_(OUT) is the output capacitance and C_(IN) is theinput capacitance of the buffer. The cost function operates to balancethe benefits from a shorter delay with benefits from a faster edge rate.For instances, in some situations, it may be more desirable to select abuffer with slightly more delay but a much larger capacitive gain (i.e.,capable of boosting the edge rate) over a buffer with less delay but arelatively small capacitive gain (slow edge rate). Thus, a buffer withthe best cost characteristics should be one providing the shortest delaytime and the fastest edge rate. The optimal driver selection method ofthe present invention will be described in more detail below.

After buffers are selected for each cluster (step 283), the clock treeinsertion process determines if the root node can drive all of thebuffers in the current level of buffers (step 284). The determination ismade based on whether the root node can drive all of the buffers at thecurrent level within the required max delay and max trans constraints.For typical integrated circuit designs, the root node is generally notable to drive all of the buffers formed by clustering the clockendpoints. Therefore, the clock tree insert process continues by addingone or more level of buffers to the buffer tree.

Thus, at step 285, the clustering operation is performed using thebuffers at the previous buffer level as the clustering nodes. Theclustering operation operates in the same manner as described in FIG. 10while using the buffer insertion points as the clustering nodes. As aresult of the clustering operation in step 285, a second level ofbuffers is formed consisting of buffers driving a number of bufferswithin a cluster. In fact, the clustering operation (step 285) and thebuffer selection and insertion process (steps 282 and 283) are repeatedrecursively to group the buffers at each level for forming a multi-levelbuffer tree. After the addition of each level of buffers, determinationstep 284 checks to see if the root node can drive all of the buffers atthat level within the required max delay and max trans constraints. Ifnot, another level of buffers is added to speed up the clock and tosharpen the clock edges until the criteria are met. The clusteringoperation of the buffers is completed when the root node is able todrive all of the buffers in a given level within the specified timingconstraints. A clock tree is thus constructed (step 286).

FIG. 11 illustrates a clock tree constructed to minimize the maximuminsertion delay using the clock tree insertion process of the presentinvention. A clock tree 320 connects root node 293 to the clockendpoints through a series of buffers at several buffer levels. Throughthe use of the clustering operation, clock tree 230 balances betweenendpoints in spare regions and endpoints in dense regions by includingmore clusters and more levels of buffers in the dense region. In FIG.11, clock tree 320 includes three levels of buffers driving fiveclusters of clock endpoints. A buffer 322 driving cluster no. 1represents the fastest path of the clock signal from root node 293 tothe endpoints in cluster no. 1. A buffer 324 driving cluster no. 5represents the slowest path of the clock signal from root node 293 tothe endpoints in cluster no. 5. Through the use of the cost function inthe buffer selection process, the clock tree insertion process minimizesthe insertion delay even in the slowest path so that clock tree 320 notonly meets the max delay constraint but minimizes the maximum insertiondelay to any endpoints as much as possible. Of course, the clock treealways meets the transition time constraint (max trans) at allendpoints.

Analyze and Correct Clock Skew Violations

Returning to FIG. 5, after a clock tree (such as clock tree 320) isconstructed in step 246, the clock tree insertion process continues byanalyzing the clock skew of the clock tree and correcting any clock skewviolations (step 248).

As described above, clock skew measures the difference between thefastest arrival time and slowest arrival time of the clock signal in theclock tree. Clock tree specification 210 includes a max skew constraintdefining the maximum value for the clock skew, that is, the maximumdifference between the fastest arrival time and the slowest arrival timein the clock tree. FIG. 12 is another representation of the clock treein FIG. 11 illustrating the connection of the clock tree to sequentiallogic gates as clock endpoints. Clock tree 320 is illustrated insimplified form in FIG. 12 and does not include all the levels ofbuffers that would be present in the clock tree. In FIG. 12, clock tree320 drives the gate terminal of a latch 332. An arrival time t_(AR1)associated with latch 332 can be measured at the Q output terminal ofthe latch. Clock tree 320 also drives the clock terminal of a flip-flop336 with associated arrival time t_(ARN) measured at the Q outputterminal of the flip-flop. By measuring the arrival times at all of theendpoints, a plot of the arrival times for the endpoints can beobtained, as shown in FIG. 13. Referring to FIG. 13, curve 338 denotesthe arrival times of the clock signal in clock tree 320 across N clockendpoints. The difference between the fastest arrival time and theslowest arrival time is the clock skew (t_(Skew)). Note that in theclock construction step (step 246), clock tree 320 is constructed sothat the slowest arrival time is as small as possible. Therefore, if theclock skew of clock tree 320 violates the max skew constraints, skewsolver module 203 is engaged to correct the clock skew violation. Clockskew correction is applied by slowing down the fastest arrival times soas to compress curve 338 and reduce the clock skew. The clock arrivaltimes are slowed down by adding delays at buffers associated with thefastest arrival times.

FIG. 14 includes three timing diagrams illustrating the arrival times atthe clock endpoints of clock tree 320 at various steps of the clock treeinsertion process. Timing diagram (a) in FIG. 14 illustrates the arrivaltimes of clock tree 320 after the clock tree construction step 246. Thetiming constraints min delay, max delay and max skew are shown in FIG.14 to illustrate the timing constraints the clock tree must meet.Referring to timing diagram (a), in the present illustration, clock tree320 has a maximum insertion delay of t_(Slow1) (the slowest arrivaltime) and a minimum insertion delay of t_(fast1) (the fastest arrivaltime). While the maximum insertion delay t_(slow1) is less than the maxdelay constraint, the clock skew t_(Skew) of clock tree 320 exceeds themax skew constraint. Therefore, clock skew correction is required.

FIG. 15 is a flow chart illustrating the clock skew correction processaccording to one embodiment of the present invention. Skew solver module203 operates the clock skew correction process to detect and correctclock skew violations. Referring to FIG. 15, clock skew correctionprocess 400 begins by elaborating all possible skew intervals for eachcluster and each group of clusters in clock tree 320 (step 402). Theconcept of “skew intervals” will be explained with reference to FIGS. 11and 16.

Referring to FIG. 11, each cluster of clock endpoints driven by a bufferwill have an associated spread of clock signal arrival times from rootnode 293. A “skew interval” is the spread of clock signal arrival timesfor a cluster of endpoints or for a group of clusters. The spread ofarrival times (skew intervals) for clusters nos. 1 to 5 of clock tree320 is depicted in the timing diagram in FIG. 16. Referring to FIG. 16,a bar 422 represents the skew interval for cluster no. 1. Since clusterno. 1 is in the fastest path of the clock signal, the fastest arrivaltime in cluster no. 1 is the arrival time t_(fast1) of clock tree 320.The skew intervals for cluster nos. 2 to 5 are also shown in FIG. 16. Askew interval can also be formed by grouping two or more clusters. Inaccordance with the present invention, two clusters can be grouped iftheir associated buffers share a common node such as any delayintroduced at the common node will affect the arrival times at theendpoints of both clusters. For example, referring to FIG. 11, clusterno. 4 is driven by a buffer 325 and cluster no. 5 is driven by buffer324. Both buffers 324 and 325 share a common node 326. Any delayintroduced at node 326 will affect the arrival times at the endpoints ofcluster nos. 4 and 5. Therefore, a skew interval can be expressed forcluster nos. 4 and 5. Referring to FIG. 16, a bar 424 represents theskew interval for cluster nos. 4 and 5. Another possible grouping ofclusters is cluster nos. 2 and 3. The buffers driving cluster nos. 2 and3 share a common node denoted by a dotted circle 327. The skew intervalfor cluster nos. 2 and 3 is shown as a bar 426 in FIG. 16. Otherpossible skew intervals for clock tree 320 include a skew interval forcluster nos. 2, 4 and 5, a skew interval for cluster nos. 3, 4 and 5, askew interval for cluster nos. 2, 3, 4 and 5, and a skew interval forcluster nos. 1, 2, 3, 4 and 5 where the common node is root node 293.

At step 402 of clock skew correction process 400 (FIG. 15), process 400elaborates all possible skew intervals for clock tree 320. Process 400also identifies a buffer insertion point for each skew interval. For askew interval of one cluster, the buffer insertion point is the inputnode to the buffer driving the cluster. For a skew interval of two ormore clusters, the buffer insertion point is the common node of theclusters or the input node of the buffer driving the common node. Forexample, for the skew interval for cluster nos. 4 and 5, the bufferinsertion point is node 326 or input node to buffer 328.

Then, process 400 computes a “ΔDelay” value for each skew interval (step404). The computation is performed in a bottom-up method. That is,ΔDelay values are computed at the lowest level of the clock tree (theclock endpoints) first and then the computation moves up towards the toplevel (the root node) of the clock tree. The use of the bottom-up methodimproves computational efficiency.

In accordance with the present invention, “ΔDelay” is defined as themaximum insertable delay which can be added to a skew interval withoutcausing a max delay violation. Referring to FIG. 16, ΔDelay value is themaximum delay amount which each skew interval can be pushed back (orslowed down) without exceeding the max delay constraint. The ΔDelayvalue for a skew interval i can be computed as follows:ΔDelay_(i)=Max Delay−(Min_(i)+Skew_(i)),where Max Delay is the max delay timing constraint, Min_(i) is thefastest arrival time in the skew interval i, and Skew_(i) is the skew(or spread of arrival times) of the skew interval i. Skew_(i) istherefore the difference between the fastest arrival time and theslowest arrival time within a skew interval i. Using the equation forΔDelay given above, the ΔDelay values for all the skew intervals whichhave been elaborated can be computed.

Next, process 400 compute the current skew of the clock tree (step 406).The current skew for clock tree 320 is t_(Skew) which is the differencebetween the fastest arrival time (t_(fast1)) and the slowest arrivaltime (t_(slow1)). Then, at step 408, process 400 determines if thecurrent skew exceeds the max skew constraint imposed by the clock treespecification. If the current skew is within the max skew constraint,the clock skew correction process terminates (step 410). Referring totiming diagram (a) in FIG. 14, the current skew t_(Skew) for clock tree320 exceeds the max skew constraint, therefore process 400 proceeds tocorrect the clock skew violation.

At step 412, process 400 apportions ΔDelay values for unmarked buffersin the clock tree. At the commencement of process 400, all buffers inclock tree 320 are unmarked. The criteria for marking a buffer inprocess 400 will be explained in more detail below. In the clock skewcorrection process, ΔDelay values are apportioned so that delays can beintroduced optimally in the clock tree for correcting the clock skewviolation. The process for apportioning ΔDelay will be explained withreference to FIG. 17.

Apportioning ΔDelay is the process of determining a common ΔDelay valuethat is shared among two or more clusters that share a common node andassigning the common ΔDelay value to a buffer at the parent buffer ofthe clusters. Referring to FIG. 17, a portion of clock tree 320 is shownincluding buffers 432 and 434 which may be each driving a cluster ofclock endpoints or each driving buffers at a lower level of the clocktree. At buffer 432, a ΔDelay value of 15 is computed. At buffer 434, aΔDelay value of 10 is computed. (For the purpose of the presentdescription, the unit of the delay value is arbitrary and is thereforenot listed. In typical applications, the delay value can be representedin units of capacitance, such as pico-farad, or in units of time, suchas nano-second.) If clock skew correction is applied at buffers 432 and434, a total delay value of 25 needs to be introduced to correct theclock skew violation.

However, because buffers 432 and 434 share a common node 435 driven by abuffer 430, their ΔDelay values can be apportioned. The common ΔDelayvalue of buffers 432 and 434 is 10. The clock skew correction process ofthe present invention will apportion the common ΔDelay value of buffers432 and 434 and assign the common ΔDelay value to buffer 430 drivingcommon node 435. As shown in FIG. 17, after the apportionment, a ΔDelayvalue of 10 is assigned to buffer 430. As a result of the apportionment,the ΔDelay value at buffer 434 is now zero and the ΔDelay value atbuffer 432 is now 5. To correct clock skew violations after theapportionment, a total delay of only 15, as compared to a delay value of25 previously, is needed to be added to the clock tree. By reducing theamount of delay to be introduced for clock skew correction, a smallerbuffer can be used and less silicon area is consumed. In summary,apportioning ΔDelay in clock tree 320 has the advantage of ensuring thatonly the minimum amount of delay is added to the clock tree forcorrecting clock skew violations.

In accordance with the present invention, the process for apportioningΔDelay follows two basic rules. First, in apportioning the common ΔDelayvalues, the drive strength of the buffer set is considered to avoidobtaining infeasible ΔDelay values. Infeasible ΔDelay values are delayvalues which are not supported by any buffer or any combination ofbuffers in the buffer set. For example, referring again to FIG. 17, ifbuffer 432 has a ΔDelay value of 10.5 and buffer 434 has a ΔDelay valueof 10, then their common ΔDelay value of 10 is not apportioned to buffer430 if there is no buffer in the buffer set which can give a delay of0.5, the remaining delay value, to buffer 432.

Second, before apportioning the ΔDelay values, the ΔDelay values arelimited to the amount of skew correction needed to meet the max skewconstraint. The amount of skew correction, ΔSkew, is the differencebetween the current skew of the clock tree and the target skew (maxskew). That is, ΔSkew is given by:ΔSkew=t _(skew)−Max Skew,where t_(Skew) is the current skew of the clock tree and Max Skew is themax skew constraint imposed by the clock tree specification. Anycomputed ΔDelay values should be less than or equal to ΔSkew becauseΔSkew is the maximum skew correction that is needed for the clock treeto meet timing constraints. In the present embodiment, any ΔDelay valuethat is greater than ΔSkew is set to equal to ΔSkew.

Returning to FIG. 15, having now computed and apportioned the ΔDelayvalues for all buffers in the clock tree (step 412), clock skewcorrection process 400 can then proceed to solve the clock skewviolations in the clock tree.

At step 414, process 400 proceeds to select the buffer with the largestΔDelay value affecting the fastest node in the clock tree. For example,referring to FIG. 16, cluster no. 1, driven by buffer 322, is thefastest node in clock tree 320. If the ΔDelay value for cluster no. 1(bar 422) is the largest ΔDelay value, then buffer 322 is selected.

Next, at step 416, process 400 operates to solve the clock skewviolation at the selected buffer by adding the desired amount of delayat the selected buffer. The desired amount of delay is the ΔDelay valueof the selected buffer. In the present embodiment, three methods ofadding delay are used. The delay can be added by adding a buffer fromthe buffer set having the required amount of delay. The buffer can bepositioned before or after the selected buffer and can be positioned atany distance from the selected buffer. The delay can also be added byresizing the selected buffer. Resizing means replacing the selectedbuffer with another buffer in the buffer set that is larger or smallerin size than the selected buffer. For example, if the selected buffer isreplaced with a smaller buffer, the edge rate of the clock signal willbe reduced and thus the delay is increased. Lastly, the delay can beadded by repositioning the selected buffer. Repositioning the selectedbuffer adds delay through adding wire delay from the additional wiring.Referring to FIG. 16, by adding delay to buffer 322 driving cluster no.1, bar 422 will be shifted to the right so that even the fastest arrivaltime for cluster no. 1 will be within the max skew timing constraint.

At step 418, process 400 determines if step 416 is successful in addingdelay at the selected buffer. Process 400 may not be able to add thedesired amount of delay (ΔDelay) to the selected buffer. One reason whydelay cannot be added is that process 400 cannot find an appropriatebuffer to introduce the desired delay. Another reason why delay cannotbe added is that process 400 cannot find a location to place the newbuffer. The placement of the existing integrated circuit design may betoo dense for process 400 to find a reasonable location to place thebuffer or the placement of the buffer may be prevented by the presenceof obstructions, such as a large memory block, near the intended bufferinsertion point. If the desired amount of delay cannot be added, thenprocess 400 marks the buffer as non-apportionable (step 420). Marking abuffer as non-apportionable will prevent any apportionment (step 412) totake pace at that buffer in the next iteration of process 400. Bypreventing apportionment, process 400 will not try to apportion theΔDelay values in the next iteration so that the clock skew violation canbe solved at each constituent buffer. Referring to FIG. 17, if step 416fails to find a buffer to add the common ΔDelay value of 10 to buffer430, then at the next iteration, process 400 will not apportion theΔDelay values and instead will try to add the ΔDelay values, 15 and 10,at each of buffer 432 and 434.

Returning to FIG. 15, if process 400 is successful in adding delay (step418), or if process 400 cannot add delay and the selected buffer ismarked as non-apportionable (step 420), clock skew correction process400 iterates by repeating steps 402 to 420 until the clock skew of theclock tree no longer violates the max skew constraint.

The iteration of clock skew correction process 400 can be explained withreference to FIG. 16. For example, in the first iteration, process 400adds delay to cluster no. 1 so that bar 422 is moved to within the maxskew constraint. That is, bar 422 is moved so that the fastest arrivaltime (the left edge of bar 422) is greater than or equal to a time t_(s)where t_(s)−t_(slow1)−max skew. Having solved the clock skew violationat cluster no. 1, cluster no. 2 becomes the next clock skew violation tobe solved. However, if cluster no. 2 is corrected individually, apartfrom cluster no. 3, the correction of cluster no. 2 and subsequentlycluster no. 3 may result in a large delay being added to the clock tree.Instead, in the second iteration, process 400 has apportioned the ΔDelayvalue at cluster nos. 2 and 3 so that process 400 first corrects theskew interval for the two clusters together (bar 426). After addingΔDelay value at the common buffer of cluster nos. 2 and 3, cluster no. 2may have remaining ΔDelay which needs to be corrected. In the thirditeration, process 400 can then add the remaining ΔDelay to cluster no.2. In this manner, clock skew violations in the clock tree arecorrected.

Timing diagram (b) in FIG. 14 illustrates the result of the clock skewcorrection process on clock tree 320. After the operation of the clockskew correction process, the previously fastest arrival time of clocktree 320, t_(fast1), has been slowed down to a new fastest arrival timet_(fast2). The clock skew t_(skew) of clock tree 320,t_(slow1)−t_(fast2), is now within the max skew constraint.

In the clock skew correction process, the only correction made is theaddition of delays to buffers with the fastest arrival times to slowdown the clock tree and compress the clock skew. This clock skewcorrection methodology is possible because the clock tree, asconstructed, is made as fast as possible. The slowest arrival time,t_(slow1), is within the max delay constraint and is “fixed.” Therefore,the slowest arrival time t_(slow1) cannot be speed up any further tocompress the clock skew. The clock skew correction process can focusonly on adding delays to the fastest arrival times for correcting theclock skew.

Analyze and Correct Min Delay Violation

Returning to FIG. 5, up to step 248, the clock tree insertion processhas constructed a clock tree meeting max delay, max skew, as well as maxtrans constraints. The clock tree insertion process continues byanalyzing the clock tree and correcting any min delay violations (step250).

Referring to timing diagram (b) of FIG. 14, after the clock skewcorrection, clock tree 320 now has a slowest arrival time t_(slow1)which is less than the max delay constraint and a clock skew t_(skew)which is equal to or less than the max skew constraint. However, thefastest arrival time t_(fast2) of clock tree 320 is less than min delay,thus violating the min delay constraint.

In general, a clock tree specification specifies a max skew that is lessthan the difference between the max delay and the min delay. Therefore,by first meeting the max delay and max skew constraints, any min delayviolation can be corrected by adding delay to the root node of the clocktree so that the delay for the entire clock tree is increased. Referringto timing diagram (c) of FIG. 14, delaying the entire clock tree has theeffect of sliding the arrival times of clock tree 320 to the right untilall of the arrival times for the clock tree are greater than the mindelay constraint. The amount of delay to add for correcting min delayviolations is the difference between the min delay constraint and thefastest arrival times of the clock tree. In the present example, theamount of delay to be added is (min delay−t_(fast2))

Alternately, min delay violations can also be corrected by adding delayto primary nodes of the clock tree. The primary nodes of the clock treeare nodes of the buffer tree just below the root node. When delay isadded to the primary nodes, the delay time for part of the clock tree isincreased with the net result that the clock skew of the clock tree isreduced. The min delay violations can thus be solved.

Min delay solver module 204 of clock tree insertion system 200 operatesto correct the min delay violations. The operation of the min delaycorrection process is analogous to the max skew correction processexcept that delay is added at the root node or the primary buffers ofthe clock tree. In the present description, the primary buffers of clocktree 320 refer to the buffers driving the primary nodes of the clocktree, that is, buffers at levels just below the root node. For example,referring to FIG. 11, the primary buffers can include buffers 321 and322 which are at a buffer level just below root node. Delays added toboth buffers 321 and 322 will affect the entire clock tree. Alternately,delays added to just buffer 321 but not buffer 322 will only affectdelay times of clock tree nodes driven by buffer 321.

FIG. 18 is a flow chart illustrating the min delay correction processaccording to one embodiment of the present invention. Referring to FIG.18, min delay correction process 450 starts by determining the amount ofmin delay violation to be corrected in the clock tree (step 452). Asdescribed above, in the present example, the amount of min delayviolation is (min delay−t_(fast2)) (timing diagram (c) in FIG. 14).Then, process 450 proceeds to add the requisite amount of delay at theroot node of the clock tree (step 454). Next, process 450 checks to seeif the clock tree meets all of the timing constraints specified in theclock tree specification (step 456).

If all of the timing constraints are met (step 458), the min delayviolation has been corrected without introducing other violations andprocess 450 terminates (step 460). If adding delay at the root nodecannot solve the min delay violation or other timing violations (such asmax trans) are introduced (step 458), then process 450 proceeds toselect buffers at the next level of the clock tree (step 462). Process450 adds delay at the next level of buffers to attempt to solve the mindelay violations (step 464). Process 450 repeats at step 456 forchecking whether the clock tree meets all of the timing constraints.Process 450 iterates steps 456 and 464 until the min delay violationsare corrected without introducing other timing violations.

Returning to timing diagram (c) of FIG. 14, after the operation of themin delay correction process (step 250 of FIG. 5), the arrival times forclock tree 320 are shifted so that all of the arrival times are greaterthan min delay. Specifically, clock tree 320 now has a fastest arrivaltime of t_(fast3) which is greater than min delay, a slowest arrivaltime of t_(slow2) which is less than max delay, and a clock skewt_(skew) of (t_(slow2)−t_(fast3)) that is equal to or less than maxskew.

Returning to FIG. 5, clock tree 320 for integrated circuit design 290has now been constructed. The clock tree insertion process is complete.At step 252, the buffers, including non-inverting buffers or inverters,can now be added to the netlist and the placement file. Clock treeinsertion system 200 outputs a netlist 218 including the buffers of theclock tree and a placement file 220 including the buffers of the clocktree. The netlist and placement files are used in the subsequent designprocess for routing and verifying the design, as shown in FIG. 1.

Advantages

As described above, the H-tree methodology attempts to construct a clocktree with balance loading. The H-tree methodology relies on the wiredistance as a proxy for load capacitance. By approximately balancing thewire distance between the root node to each endpoint, the capacitiveloading of the tree branches is assumed to be balanced as well. In themanner, the H-tree balances the clock signal delay to each endpoint.However, as described above, the H-tree methodology is not satisfactorybecause balancing the wire distances does not always mean balancing theload.

In accordance with the present invention, the clock tree insertionsystem and method construct a clock tree by directly balancing thedelay. The clock tree insertion system and method of the presentinvention realize numerous advantages not achievable by conventionalclock tree methodologies.

First, because the clock tree is constructed by evaluating the clocksignal delays rather than using a proxy for the delay, such as wirelength, the clock tree insertion system and method can be used toconstruct a clock tree that meets tighter timing constraints.

More importantly, the clock tree constructed according the method of thepresent invention can be made faster (higher operating frequency) thanclock trees constructed using conventional methods, such as the H-treemethodology, because the method of the present invention does notintroduce dummy loads in constructing the clock tree. The use of thedummy loads for load balancing in the conventional H-tree methodologyadds to the total loading the clock tree has to drive, thus slowing downand limiting the frequency of the clock signal.

A clock tree constructed in accordance with the method of the presentinvention provides reasonable stability across manufacturing andoperational environment variations. Thus, the clock tree providespredictable delays, thereby improving the robustness of the integratedcircuit design. Furthermore, the stability can be achieved “atspeed”—i.e., at the operating frequency of the integrated circuitdesign.

A clock tree constructed using the system and method of the presentinvention uses optimally sized buffers at optimally placed insertionpoint. The clock tree thus requires less silicon area to implement andconsumes less power.

In summary, the clock tree insertion system and method of the presentinvention can be applied in integrated circuit designs to build a robustclock tree, especially for designs employing the deep sub-microns orbelow fabrication technologies.

Zero-Skew Buffer Insertion Point Computation

In constructing a clock tree in accordance with the clock tree insertionmethod of the present invention (step 246 of FIG. 5), a clusteringoperation is performed and in each cluster, whether comprising of clockendpoints or buffers at a lower level of the clock tree, a bufferinsertion point is determined for positioning a buffer for driving theclustering nodes in the cluster (step 282 in FIG. 8). A traditionalmethod for determining the buffer insertion point for a group of objectsplaces the insertion point at the geometric center of the area occupiedby the objects. For example, in the H-Tree methodology discussed above,the integrated circuit design is divided into regions and the geometriccenter of each region is used as the buffer insertion point for thatregion. The geometric center is the arithmetic mean of the distancesfrom the buffer insertion point to all endpoints within a region. Othertraditional methods involve using iterative computation to search for aposition that balances the clock skew to all of the endpoints. However,the traditional methods are generally not satisfactory, particularlywhen the region of interest is large. The traditional methods may give abuffer insertion point which has a larger than necessary delay time ormay result in a large local clock skew within the region.

According to one aspect of the present invention, the buffer insertionpoint for each cluster is positioned at a “zero-skew” point within acluster. In accordance with the present invention, a zero-skew pointwithin a cluster is the position in an area occupied by the clusterwhere the insertion of the buffer gives the smallest local clock skewfor the cluster. That is, the zero-skew point minimizes the spread ofthe arrival times for the clustering nodes within the cluster.

In accordance with the present invention, a method for computing azero-skew buffer insertion point in a cluster involves applyingminimization of the variance to a function describing the distance fromeach clustering node to the buffer insertion point. By minimizing thevariance of the distances from the clustering nodes to the bufferinsertion point, the variance of the arrival times is also minimized.The method for computing a zero-skew buffer insertion point will now bedescribed. For the purpose of the present description, an integratedcircuit design (such as design 290 in FIG. 9 a) is assumed to be on aCartesian plane with the origin of the position coordinates at thelower-left corner of the design. Any position within the integratedcircuit design can be assigned an coordinate (x, y). The coordinate forthe zero-skew buffer insertion point will be denoted as (x_(b), y_(b)).

First, given a cluster of N clustering nodes, a function describing adistance d from each clustering node to the position (x_(b), y_(b)) ofthe zero-skew insertion point is written. In the Euclidean distancemetric, the function f (d_(i)) is expressed as follows:f(d _(i))=√{square root over ((x _(i) −x _(b))²+(y _(i) −y_(b))²)}{square root over ((x _(i) −x _(b))²+(y _(i) −y _(b))²)},  Eq.(1)where (x_(i), y_(i)) denotes the coordinate of any clustering node i inthe cluster of N clustering nodes. For the rectilinear distance metric,the function f(d_(i)) is expressed as follows:f(d _(i))=|(x _(i) −x _(b))|+|(y _(i) −y _(b))|.  Eq. (2)

Next, the equation for computing the variance is applied to the functionf(d_(i)) as follows: $\begin{matrix}{{\left( {N - 1} \right)\sigma} = {{\sum\limits^{\;}\;\left( {f\left( d_{i} \right)} \right)^{2}} - {\frac{1}{N}\left( {\sum\limits^{\;}\;{f({di})}} \right)^{2}}}} & {{Eq}.\mspace{14mu}(3)}\end{matrix}$

Then, minimization of the variance to the function f(d_(i)) is appliedby taking the first derivative of Equation (3) with respect to thedistance d and setting the first derivative to zero. The positioncoordinate (x_(b), y_(b)) for the buffer insertion point is then solvedfor using the first derivative of Equation (3).

To verify that the solution based on the first derivative is indeed theminimum, the second derivative of Equation (3) is taken. If the secondderivative is a positive value, then the solution based on the firstderivative is a minimum point and the solution is validated. If thesecond derivative is a negative value, then the solution based on thefirst derivative is actually a maximum point and the solution isinvalid.

By applying the function f(d_(i)) for any distance metrics in Equation(3), the minimization of variance can be performed so as to obtain theequations for computing the zero-skew buffer insertion point. In thepresent description, an one-dimensional solution using the square of theEuclidean distance metric is obtained using the method of the presentinvention. The square of the Euclidean distance metric is the square offunction f(d_(i)) of Equation (1) above. The solution providing thecoordinates for the buffer insertion point is as follows:$\begin{matrix}{{x_{b} = \frac{0.5 \times \left( {{{M1} \times {M2}} - {N \times {M3}}} \right)}{\left( {{{M1} \times {M1}} - {N \times {M2}}} \right)}},} & {{Eq}.\mspace{14mu}(4)} \\{{y_{b} = \frac{0.5 \times \left( {{{M1} \times {M2}} - {N \times {M3}}} \right)}{\left( {{{M1} \times {M1}} - {N \times {M2}}} \right)}},} & {{Eq}.\mspace{14mu}(5)}\end{matrix}$where Mk in Equation (4) is the k^(th) moment of x with respect to zero,Mk in Equation (5) is the k^(th) moment of y with respect to zero, and Nis the number of clustering nodes in the cluster. The moments Mk for thex dimension are given as follows:${{M1} = {\sum\limits_{i = 1}^{N}\; x_{i}}},{{M2} = {\sum\limits_{i = 1}^{N}\; x_{i}^{2}}},{{M3} = {\sum\limits_{i = 1}^{N}\;{x_{i}^{3}.}}}$The moments Mk for the y dimension are given as follows:${{M1} = {\sum\limits_{i = 1}^{N}\; y_{i}}},{{M2} = {\sum\limits_{i = 1}^{N}\; y_{i}^{2}}},{{M3} = {\sum\limits_{i = 1}^{N}\;{y_{i}^{3}.}}}$

Equations (4) and (5) above give the solution for computing thezero-skew buffer insertion point for an one-dimensional Euclidean space.Solutions for computing the zero-skew buffer insertion point using otherdistance metrics, such as the rectilinear space or a hybrid of Euclideanand rectilinear space, can also be expressed. Furthermore,two-dimensional solution can also be obtained. Equations (4) and (5)above give two separate one-dimensional solutions for the x and ydimensions. The one-dimensional solutions may contain errors due to somecross-term between the x and y dimensions not accounted for in thesolutions. In most applications, the one-dimensional solution isadequate for computing a satisfactory zero-skew point. However, atwo-dimensional solution can be derived if elimination of cross-termerrors is desired.

When Equations (4) and (5) are used to compute the zero-skew bufferinsertion point for a cluster, the computation can be performed using aCartesian coordinate system with the origin at the lower-left corner ofthe integrated circuit design. In another embodiment, scaling of theposition coordinates (x, y) can be continuously applied so that the cubeof the position coordinates does not exceed the maximum signed floatingpoint number representable by the computing machine. For example, themaximum signed floating point number that can be represented by a 32-bitcomputer is approximately 10³⁸. Thus, during the computation of thezero-skew buffer insertion point of the present invention, scaling canbe applied to keep the cube of any position coordinates to less than10³⁸.

The method for computing a zero-skew buffer insertion point of thepresent invention has applications beyond clock tree construction. Ingeneral, the method of the present invention can be used to determinethe zero-skew insertion point for positioning a driver in an areaoccupied by nodes that are to be driven by the driver. The driver can bea buffer, an inverter, or any other logic gates, such as a NAND gate ora NOR gate). The nodes can be input pins of logic gates receiving asignal generated by the driver. The method of the present invention canbe used to compute the zero-skew driver insertion point so that thespread of the signal arrival times at the nodes is minimized.

Match-Delay Buffer Insertion

In the clock tree insertion method of the present invention, a clocktree is constructed to be as fast as possible and then the clock tree isslowed down by adding delays at the fastest nodes in order to meet mindelay and max skew timing constraints. The traditional methods foradding delay to a node involves adding a buffer having the desired delayvalue or resizing the buffer at the node. The traditional methods foradding delay often result in a change in the load capacitance to theprevious stage. For example, if a buffer having a smaller size then thecurrent buffer is added to introduce the desired amount of delay, theinput capacitance as seen by the node upstream to the newly added bufferis now changed. In fact, the input capacitance as seen by the upstreamnode is decreased and the delay at the upstream node is decreasedbecause the buffer at the upstream node only needs to drive a smallercapacitance.

Consequently, in an effort to add a delay at the current node to slowdown the clock tree, the addition of delays may actually result inmaking the clock tree faster at other nodes of the clock tree. Thechanging of the input capacitance of the previous stage and theresultant speeding up of the clock tree can have a ripple effectthroughout the clock tree. Therefore, the traditional methods for addingdelays is undesirable because clock tree construction tends to convergevery slowly as new delay problems are created when existing problems arebeing solved.

According to another aspect of the present invention, a method for“match-delay” buffer insertion is provided to add delays at a nodewithout changing the input capacitance of the node as seen by theupstream node (or the parent node). When delays are to be added tobuffers in the clock tree for meeting min delay and max skew timingconstraints, optimally sized buffers are added at optimal locations sothat the capacitive loading to the previous stages (the parent stages)remains the same or changes only minimally. In this manner, the clocktree insertion process avoids introducing new timing violations whiletrying to cure existing violations. The match-delay buffer insertionmethod allows the clock tree insertion process to coverage more rapidlyfor constructing a clock tree meeting timing constraints.

FIG. 19 is a flowchart illustrating the match-delay buffer insertionmethod according to one embodiment of the present invention. In thepresent embodiment, match-delay buffer insertion method 500 is appliedto correct clock skew violations and is performed prior to step 402 ofclock skew correction process 400 of FIG. 15. When match-delay bufferinsertion method 500 is included in the clock tree insertion method ofthe present invention, method 500 is used to correct large delayviolations while leaving the minor delay violations for clock skewcorrection process 400 to correct. Specifically, match-delay bufferinsertion method 500 uses only addition of buffers for introducing largedelay values and do not use other methods, such as resizing the currentbuffers or repositioning the current buffers, to add delays.Subsequently, process 400 uses resizing and repositioning to introducesmall delay values to fine tune the clock skew correction. The operationof the match-delay buffer insertion method will be explained withreference to clock tree 320 in FIG. 11.

Referring to FIG. 19, steps 502 to 510 of method 500 are the same assteps 402 to 410 of process 400 of FIG. 15. However, after method 500determines that there is a clock skew violation (step 508), that is, thecurrent skew is greater than the max skew constraint, method 500 doesnot apportion the ΔDelays as in process 400. Rather, method 500 proceedsto order the endpoints by the fastest to slowest arrival times (step511). Then, method 500 performs a depth-first sweep of the buffers inthe buffer tree, selecting the deepest buffer level in the path to theclock endpoint of the fastest arrival time. The selected buffer shouldbe one that is “unmarked.” At the commencement of method 500, allbuffers in clock tree 320 are unmarked. The criteria for marking abuffer in method 500 will be explained in more detail below withreference to step 528. In the present example, buffer 322 being thebuffer at the deepest level of the fastest node, will be selected atstep 512 as the current buffer.

Having selected the current buffer for introducing delay, method 500proceeds to add delays without changing the input capacitance. At step518, method 500 first attempts to add a buffer that is the same as thecurrent buffer just before the current buffer. By adding the same bufferas the current buffer, the upstream node (root node 293 in FIG. 11) willsee the same input capacitance and thus the delay at the upstream nodewill not change. At step 520, method 500 determines if the addition ofthe same buffer before the current buffer corrects the clock-skewviolation and that the current node, as corrected, meets the timingconstraints. If so, addition of buffer is successful and method 500returns to step 502 for correcting timing violations at other nodes.

If addition of a buffer before the current buffer is not successful incorrecting the clock skew violations or causes other timing violations(step 520), method 500 proceeds to add a buffer after the current buffer(step 524). In the present embodiment, method 500 tries all buffers inthe buffer set to find a buffer which can be added after the currentbuffer for correcting the clock skew violation. The buffer added may beof a dissimilar size than that of the current buffer. But since the newbuffer is added after the current buffer, the input capacitance as seenby the upstream node remains unchanged. If the addition of the bufferafter the current buffer is successful in curing the clock skewviolation and the current node, as corrected, meets the timingconstraints (step 526), method 500 returns to step 502 to correct clockskew violations at other nodes. If the addition of the buffer after thecurrent buffer is unsuccessful, then the current buffer is marked as“non-addable” indicating that the delay cannot be introduced at thisbuffer by adding a new buffer. Instead, the “non-addable” buffers willbe corrected at process 400 where delays can be added by resizing thebuffer or repositioning the buffer.

FIGS. 20 a and 20 b illustrate the operation of the match-delay bufferinsertion method of the present invention in adding delays to a currentbuffer without changing the load as seen by the parent node. Referringto FIG. 20 a, step 518 of method 500 introduces delays by adding a newbuffer 530 that is of the same buffer type as current buffer 532 justbefore the current buffer. The physical location of new buffer 530 ischosen to be as near the physical location of current buffer 532 aspossible to avoid changing the wire capacitance. In the manner, theparent node to current buffer 532 will see almost the same inputcapacitance after the addition of new buffer 530.

Referring to FIG. 20 b, step 524 of method 500 introduces delays byadding a new buffer 534 after current buffer 532. New buffer 534 may beof a different buffer type than current buffer 532. Because the parentnode to current buffer 532 sees the same buffer 532, the inputcapacitance as seen by the parent node is unchanged. To add a givendelay, new buffer 534 can be a larger buffer than the current buffer ora smaller buffer than the current buffer. Adding a larger or smaller newbuffer after the current buffer may change the loading of the currentbuffer and accordingly changes the delay of the current buffer.Therefore, step 524 steps through all the buffers in the buffer set andselects a combination of current/new buffers which would give thedesired delay amount.

After the operation of match-delay buffer insertion method 500, theclock insertion process of the present invention can return to clockskew correct process 400 of FIG. 15 for correcting any remaining clockskew violations. In accordance with the present invention, thematch-delay buffer insertion method has the effect of curing timingviolations requiring large delay insertions (e.g. greater than 100 pf).The large delay insertions are handled exclusively by adding buffersusing the match-delay technique so that the input capacitance as seen bythe parent nodes is not disturbed. Then, the remaining small scaletiming violations can be corrected by using the resizing orrepositioning techniques where small, incremental delays can beintroduced.

The match-delay buffer insertion method of the present invention canalso be applied for correcting other timing violations, such as mindelay violations. For example, referring to FIG. 18, when min delaycorrection process 450 operates to add delays at the root node (step454) or at the primary buffer levels just below the root node (step462), process 450 can apply the match-delay buffer insertion method inadding delays. That is, steps 454 and 462 will first operate to add thesame buffer as the target buffer before the target buffer (the targetbuffer refers to the root node or the primary buffer levels where delaysare to be added). If the timing violation cannot be fixed by adding amatched buffer before the target buffer, then steps 454 and 462 willoperate to add a buffer after the target buffer. All buffers in thebuffer set will be tried to find a combination of the new buffer and thetarget buffer that would give the desired delay. If the match-delaytechnique cannot be used to cure the min delay violation, then process450 will return to its default operation where delays can be added byresizing the target buffer or repositioning the target buffer.

In the above description, the match delay buffer insertion method isapplied for introducing delays in a clock tree constructed using buffersand inverters. The match delay buffer insertion method of the presentinvention can have other applications in the design of an integratedcircuit. In general, the match delay buffer insertion method can be usedto introduce delays in any part of an integrated circuit delay wherepreservation of the input capacitance is desired. Thus, the match delaybuffer insertion method can be used for introducing delays using logicgates other than buffers and inverters. For instance, if a delay is tobe added to an NAND gate, the match delay buffer insertion method willfirst try to add the same NAND gate before the target NAND gate tointroduce the desired delay. If adding an NAND gate before the targetgate does not work, then the match delay buffer insertion method willadd a delay using any logic gate after the target NAND gate. In thismanner, the input capacitance of the target NAND gate can remainunchanged as delay is being added.

Optimal Driver Selection

In constructing a clock tree in accordance with the clock tree insertionmethod of the present invention (step 246 of FIG. 5), clusteringoperations are performed repeatedly to group clock endpoints or buffersinto clusters. In each cluster, a buffer insertion point is determined(step 282 of FIG. 8) and a buffer capable of driving the nodes withinthe cluster is selected (step 283 of FIG. 8). Typically, the buffer isselected from a list of candidate buffers defined by the user orselected by default by the clock tree insertion system.

The buffer selection process in the clock tree insertion method can begeneralized to the process of selecting a driver in a logic chain ofdrivers. The drivers can be buffers or inverters or logic gates such asNAND or NOR gates. The logic chain can be part of a clock tree, a phasedlocked loop, or any part of an integrated circuit design, such as a partof a decoder circuit. In any case, the driver selection process involvesselecting a driver which can drive the predetermined capacitive loadwithin predetermined timing constraints. In some cases, in building alogic chain, a driver is preslected and it is necessary to determine theamount of load that can be effectively coupled to the driver withoutviolating predetermined timing constraints.

Mead and Conway describes one traditional method for selecting theoptimal driver for driving a large capacitive load. (See “Introductionto VLSI Systems” by C. Mead and L. Conway, Addison-Wesley PublishingCompany, 1980, pages 10–14.) In the traditional method, to drive acapacitive load C_(L), a chain of increasingly sized drivers (buffers orinverters) is used where the last driver is large enough to drive theload capacitance C_(L) directly. In a chain of buffers, the delaythrough one stage of the chain is given as ατ, where α is the fanoutfactor for the buffer and τ is the delay time of the first buffer in thebuffer chain. Typically, the delay time τ is modeled as RC, that is, theproduct of the output resistance of the stage driving the first bufferand the input capacitance of the first buffer. For a chain of N buffers,each stage having a fanout factor of α, the total delay D_(T) for theentire buffer chain is given as:

D_(T)=NαRC, and  Eq. (6) $\begin{matrix}{{\alpha^{N} = \frac{C_{L}}{C_{IN}}},} & {{Eq}.\mspace{14mu}(7)}\end{matrix}$where C_(L) is the load capacitance driven by the chain of buffers andC_(IN) is the input capacitance of the first buffer stage. By solvingfor N in Equation (7), the total delay D_(T) can be written as:$\begin{matrix}{{D_{T} = {\alpha\;{RC}\frac{\ln\;{Cg}}{\ln\;\alpha}}},} & {{Eq}.\mspace{14mu}(8)}\end{matrix}$where Cg is C_(L)/C_(IN), which is the capacitive gain of the entirebuffer chain.

Mead and Conway concluded that to minimize the total delay D_(T), afanout factor of e (2.718) should be used for each stage. Thus, in thetraditional buffer selection method based on the analysis provided byMead and Conway, a buffer having a fanout factor of e is selected todrive each stage of the buffer chain.

While the Mead and Conway solution provides a mathematically correctmethod for selecting buffers to build a chain of buffers so that thetotal delay is minimized, the Mead and Conway solution has shortcomingsin practice. In actual implementation, the fanout factor of e predictedby Mead and Conway works well only for non-submicron NMOS technologies.As technologies advance to CMOS and to submicron technologies, the Meadand Conway solution no longer applies. In fact, for submicron CMOStechnologies, the fanout factor of e (2.718) is an incorrect value forminimizing total delay. In practice, designers using SPICE simulation ortest chip have discovered that a fanout factor of 4–6 should be used tominimized total delay. However, no closed-formed solution fordetermining the fanout factor for submicron CMOS technologies have beendeveloped and designers often rely on SPICE simulation and test chips todetermine the optimal fanout factor for use in the particular technologyof interest.

Another shortcoming of the traditional buffer selection method based onthe Mead and Conway solution concerns the use of the “RC” model for thebuffer delay τ. The RC model for delay is a linear approximation whichis not very accurate in practice. Delay through a logic gate is notstrictly the product of the output resistance (of the previous stagedriving the logic gate) and the input capacitance (of the logic gate).In fact, the buffer delay has a non-linear characteristic with respectto the output resistance and the input capacitance. Also, the linear RCmodel does not take into account the intrinsic delay of the buffer.Thus, a buffer chain constructed using the linear RC approximation fordelay is often slower than desired.

According to one aspect of the present invention, a method for optimaldriver selection is provided for selecting an optimal driver for drivinga predetermined capacitive load. The optimal driver selection methoduses a cost function that is based on the non-linear delaycharacteristics and the capacitive gain of the candidate drivers. Thecapacitive gain of a driver is defined as C_(OUT)/C_(IN) where C_(OUT)is the output capacitance driven by the driver and C_(IN) is the inputcapacitance of the driver. The cost function operates to select anoptimal driver for driving the predetermined capacitive load whichsimultaneously minimizes the delay and the amount of input capacitanceintroduced. In practice, the cost function operates to select a driverby balancing the benefits from a shorter delay with benefits from afaster edge rate. According to another aspect of the present invention,the method for optimal driver selection can be applied in selecting anoptimal load for a driver. The use of the method of the presentinvention for optimal load selection will be described in more detailbelow.

In accordance with the present invention, a cost function C for optimaldriver selection is given as: $\begin{matrix}{{C = \frac{{Stage}\mspace{14mu}{Delay}}{\ln\;\alpha}},} & {{Eq}.\mspace{14mu}(9)}\end{matrix}$where Stage Delay is the delay of a candidate driver and lnα denotes thenatural logarithm of the stage gain or the fanout factor of the driver.In the present embodiment, the stage gain of the driver is expressed asthe capacitive gain (C_(OUT)/C_(IN)) of the driver. Thus, Equation (9)can be expressed as: $\begin{matrix}{C = {\frac{{Stage}\mspace{14mu}{Delay}}{\ln\left( \frac{C_{OUT}}{C_{IN}} \right)}.}} & {{Eq}.\mspace{14mu}(10)}\end{matrix}$The cost function of the present invention is based on Equation (8)describing the total delay D_(T) of a logic chain. In Equation (8), thetotal delay is a function of the stage delay (αRC) and an inversefunction of logarithm of the fanout factor (α). The term ln(Cg) is aconstant describing the capacitive gain of the entire logic chain.

The inventor of the present invention recognizes that in order tominimize the total delay D_(T) of a logic chain, an optimal driver foreach stage should have a small stage delay but a large logarithm of thestage gain. Therefore, the cost function of Equation (10) is derived toselect a driver with the best delay value over the logarithm of thestage gain. In essence, the cost function of the present inventionselects the fastest driver with the minimum input capacitance so thatthe new driver introduces an input capacitance that is as small aspossible. By using the cost function of the present invention, a veryfast logic chain can be constructed having minimum delay and introducingminimum capacitance to the integrated circuit.

In the present embodiment, the stage delay values of the candidatedrivers are obtained from look-up tables in the cell library of thecandidate drivers. Because the cell library contains delay values whichare determined from empirical data, taking into consideration non-lineardelay characteristics and intrinsic delay values, the stage delay valuesused in the cost function computation is more accurate than thetraditional methods using a linear approximation of the driver's delay.

In one embodiment of the present invention, the optimal driver selectionmethod operates by first computing the cost function C for all thedrivers in the driver set. The driver set can be specified by thedesigner or chosen by default by the cell library. The optimal driverselection method then selects the driver with the minimum cost computedbased on the cost function. In another embodiment, instead of computingthe cost function for all the drivers in the driver set, the methodcomputes the cost function for a first driver and then performs aminimization routine for finding the driver with the minimum cost.Computational methods for minimizing a function (minimization routines)are well known in the art and any such routine can be used in theoptimal driver selection method of the present invention.

In yet another embodiment of the present invention, the optimal driverselection method uses a precomputed table for each driver containingcost values over a range of stage gain values or over a range of loadcapacitance (C_(OUT)) values. The precomputed tables can be generated bythe optimal driver selection method of the present invention or thetables can be provided in the cell library as a standard set ofparameters defining each cell in the cell library. To compute the costfunction for a given set of drivers, the optimal driver selection methodperforms a table look-up operation using the predetermined outputcapacitance C_(OUT) value. Interpolation of the table values can beperformed if the exact C_(OUT) value is not provided in the precomputedtable. When the look-up table contains cost as a function of the stagegain, a computation of the stage gain using the output capacitanceC_(OUT) value is first performed before the table look-up operation.

The operation of the optimal driver selection method will now beexplained by way of an example. Assume that a buffer is to be selectedto drive a load capacitance of C_(x) and the buffer set contains twobuffers B1 and B2, the optimal driver selection method performs a tablelook-up operation to retrieve the electrical characteristics of the twobuffers from the cell library. Assume that buffers B1 and B2 have thefollowing electrical characteristics:

Buffer C_(IN) Delay B1 0.9C_(x) 10 B2 0.1C_(x) 100where the input capacitance C_(IN) is expressed in terms of the loadcapacitance C_(X) and the delay is expressed as a generic values withoutunit for ease of illustration. In actual implementation, the inputcapacitance and the delay for the buffers will be expressed in unitscommonly used, such as pico-farad and nano-second, respectively. Havingobtained the electrical characteristics of buffers B1 and B2, the costfunction for each buffer can be computed using C_(X) as the outputcapacitance C_(OUT). The costs for buffers B1 and B2 are computed asfollows: $\begin{matrix}{{{{Cost}\;({B1})} = {\frac{10}{\ln\left( \frac{C_{X}}{0.9C_{X}} \right)} = 95}};{and}} \\{{{Cost}\;({B2})} = {\frac{100}{\ln\left( \frac{C_{X}}{0.1C_{X}} \right)} = {43.4.}}}\end{matrix}$The cost for buffer B2 is less than buffer B1, therefore buffer B2 isselected by the optimal driver selection method of the presentinvention. In the present example, buffer B2 has a larger stage delayvalue than buffer B1 but buffer B2 has a smaller input capacitance thanbuffer B1. In other words, buffer B2 has a larger stage delay butprovides a larger capacitive gain. In fact, buffer B2 has a 10 timescapacitive gain while buffer B1 only has a 1.11 times capacitive gain.The cost function of the present invention balances the benefit of ashort delay with the benefit of a larger capacitive gain (i.e., smallinput capacitance). In this example, the cost function selects a bufferwith 10 times the capacitive gain, even though the buffer has 10 timesthe delay value as the other buffer.

The above example illustrates one embodiment of the optimal driverselection method of the present invention. In other embodiments, thecell library for buffers B1 and B2 may contain precomputed costs as afunction of output capacitance C_(OUT). Thus, the optimal driverselection method operates by indexing the precomputed values usingcapacitance C_(X) and retrieving the cost of the buffer. Interpolationof table values may be performed to obtain the cost of the buffer for anoutput capacitance of C_(X). In another embodiment, the cell library forbuffers B1 and B2 may contain precomputed costs as a function of thecapacitive gain (C_(OUT)/C_(IN)). In that case, the optimal driverselection method computes the capacitive gain for each buffer and usesthe capacitive gain values to index the precomputed table to retrievethe cost for the buffer.

The application of the cost function of the present invention in theselection of an optimal driver has many advantages. First, the costfunction is applied to trade-off delay and input capacitance optimallyin the selection of a driver so that a logic chain can be constructed asfast as possible while the total capacitance for the logic chain is madeas small as possible. That is, by selecting a driver with the best delay(smallest delay value) and the largest stage gain (largest capacitivegain), the cost function selects a driver that is fast and introducesthe smallest capacitance.

Second, the cost function is applied to ensure that, when a driver isselected, the capacitance presented to the parent stage driving thedriver is the smallest capacitance possible while maintaining the bestdelay performance. Presenting the smallest capacitance to the parentstage is particularly important when the driver of the parent stage isnot yet determined. If a first buffer in the chain is selected so thatthe capacitance presented to the parent stage is too large, it maybecome impossible to find a second buffer which can drive the firstbuffer within the predetermined timing constraints. Referring to theexample above, the larger capacitive gain (or the smaller inputcapacitance) of buffer B2 means that the parent stage driving buffer B2only needs to drive a small capacitance value, as compared to thecapacitance value of buffer B1. Therefore, buffer B2 is preferred overbuffer B1.

Third, the optimal driver selection method of the present inventionprovides more accurate driver selection results than the traditionalmethods because the method of the present invention uses actual delayvalues for the drivers, as opposed to a linear approximation used in thetraditional methods. Also, the result is more accurate because themethod of the present invention numerically minimizes the cost functionfor the candidate drivers in the driver set. The method of the presentinvention does not rely on precomputed fanout factor which is generallyapplicable for the technology but not specifically computed for thedrivers of interest.

The optimal buffer selection method of the present invention has manyapplications. In one embodiment, the optimal driver selection method isapplied to the clock tree insertion method of the present invention forselecting a buffer to drive nodes that are grouped into a cluster. Theload capacitance for the buffer can be determined from the number ofnodes within the cluster and the input capacitance of each of the nodes.In one embodiment, the cost function is computed for each buffer in thebuffer list specified for use by the clock tree. In another embodiment,the cost is retrieved by a table look-up operation using the loadcapacitance to index the precomputed cost versus load capacitance tablefor each buffer. The buffer with the smallest cost is selected as thebuffer to drive the cluster. By applying the optimal driver selectionmethod to the selection of buffers in the clock tree insertion method ofthe present invention, a clock tree with minimized maximum insertiondelay can be constructed. Also, in the clock tree insertion process, ateach stage where a buffer is selected for driving a cluster, the parentstage is not yet determined. The optimal driver selection method choosesa buffer with the smallest input capacitance possible to ensure that theparent stage will see the smallest load possible.

In another embodiment, the optimal driver selection method is applied todetermine the size of a logic gate for use in a chain of logic. Forexample, in a given chain of logic, the optimal driver selection methodcan be used to determine the size of a logic gate to be used to drive agiven load. The optimal driver selection method is applied to ensurethat the selected logic gate minimizes the delay while keeping the inputcapacitance introduced to the parent stage as small as possible. Forexample, in a chain of NAND gates, it is necessary to determine the sizeof a first NAND gate in the chain driving a load capacitance C_(L). Thecost function is applied to the NAND gates in the cell library to findthe NAND gate with the smallest cost. In computing the cost function,the stage delay is the delay of the critical path through the NAND gate.For example, if the “A” input pin of the NAND gate is in the criticalpath, the delay from “A” to the output of the NAND gate is used as thestage delay. The input capacitance of input pin “A” is used as the inputcapacitance C_(IN) of the cost function. In this manner, a NAND gate ofthe appropriate size is selected where the NAND gate has the minimumdelay and the smallest input capacitance.

In yet another embodiment, the optimal driver selection method isapplied for optimal load selection. That is, the optimal load selectionmethod applies the cost function to determine the optimal load a givenlogic gate can drive while maintaining the best delay performance. Forinstance, in an integrated circuit design, a preselected logic gate hasto drive a large fanout. The optimal load selection method is applied todetermine how much load each logic gate can drive so that theappropriate number of the preselected logic gate can be included fordriving the large fanout. In another example, in constructing a clocktree, if the clock tree specification includes only one buffer type inthe buffer list available to build the clock tree, then the optimal loadselection method is applied to determine the amount of nodes each buffercan drive in the clock tree.

In operation, the optimal load selection method is applied for aselected logic gate. The optimal load selection method uses theprecomputed cost versus C_(OUT) table for the selected logic gate in thecell library. From the cost versus C_(OUT) table, the optimal loadselection method selects the output capacitance C_(OUT) value whichgives the minimum cost. Interpolation of the table values may be neededto determine a C_(OUT) with minimum cost. The output capacitance valueC_(OUT) can then be used as the desired load selected for the selectedlogic gate.

The above detailed descriptions are provided to illustrate specificembodiments of the present invention and are not intended to belimiting. Numerous modifications and variations within the scope of thepresent invention are possible. For instance, while the flowcharts inthe figures of the present invention illustrate certain processsequence, one of ordinary skill in the art, upon being apprised of thepresent invention, would know that some of the process sequence can berearranged to achieve the same result. The process sequence in theflowcharts are illustrative only. The present invention is defined bythe appended claims.

1. A method for determining a first load capacitance to be driven by adriver, said method comprising: providing a set of cost values as afunction of load capacitance based on a cost function for said driver,said cost function being directly proportional to a delay of said driverand inversely proportional to the logarithm of a stage gain of saiddriver; and selecting said load capacitance associated with the smallestcost value as said first load capacitance.
 2. The method of claim 1,wherein said driver comprises a buffer or an inverter.
 3. The method ofclaim 1, wherein said driver comprises a NAND gate or a NOR gate.
 4. Themethod of claim 1, wherein said providing a set of cost values as afunction of load capacitance comprises computing said set of cost valuesover a range of load capacitance values using said cost function, andstoring said set of cost values in a precomputed table, said precomputedtable being associated with said driver in a cell library.
 5. The methodof claim 1, wherein said providing a set of cost values as a function ofload capacitance comprises providing a set of cost values as a functionof stage gain, said stage gain being an output capacitance driven bysaid driver divided by an input capacitance of said driver.
 6. Themethod of claim 5, wherein said providing a set of cost values as afunction of stage gain comprises computing said set of cost values overa range of stage gain values using said cost function, and storing saidset of cost values in a precomputed table, said precomputed table beingassociated with said driver in a cell library.
 7. The method of claim 1,wherein said cost function is given as${C = \frac{StageDelay}{\ln\;\left( \frac{Cout}{Cin} \right)}},$ where Cis said cost, said stage delay is said delay of said driver, C_(OUT) isan output capacitance driven by said driver and C_(in) is an inputcapacitance of said driver, said output capacitance being said loadcapacitance.